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Carbon-basis closure for polymer degradation compares the amount of carbon initially introduced in a polymer with the carbon recovered in all measured products and residues. It avoids confusing incorporated water with recovered original polymer mass, while requiring dissolved and gaseous products to be counted as well as retained solids.

On a consistent specimen-carbon basis, writeThe measured recovery is the sum of the first four terms divided by $C_0$. Specify whether each $C$ denotes carbon mass or amount of substance; numerator and denominator must use the same units. Carbon from medium, inoculum, solvent or contamination must be separated from specimen-derived carbon.

An original polyglycolic acid example begins with one millimole of repeat-unit inventory, containing two millimoles of carbon atoms, approximately 24.02 mg of carbon. Hydrolysis to one millimole of glycolic acid preserves those carbon atoms while incorporating water. The product's larger total mass is therefore not extra carbon recovery. The manufacturer's repeat structure and decomposition diagram identify that chemical relationship.^[ref]

If some products become carbon dioxide, convert measured gas mass to carbon mass before adding it to residue carbon:For an illustrative initial 24 mg of carbon, suppose corrected measurements recover 12 mg in solid, 6 mg dissolved and approximately 3 mg in carbon dioxide. Recovery is $21/24=87.5\%$, leaving 3 mg unaccounted. Approximately 11 mg of carbon dioxide contains 3 mg of carbon; adding that full gas mass to solid and dissolved carbon would mix bases.

A concrete primary apparatus is the OECD 301 B carbon-dioxide evolution test. It aerates inoculated mineral medium with carbon-dioxide-free air at a controlled rate, traps evolved gas in barium or sodium hydroxide, and determines it by titration or inorganic-carbon measurement. Blank inoculum contributions are subtracted.^[ref] These operations explain why inlet scrubbing, gas collection and blank correction belong to the measurement rather than being optional bookkeeping.

The guideline is a chemical biodegradability test, not proof that every polymer shape or formulation meets its applicability conditions. Its general section requires attention to solubility, volatility, adsorption and composition.^[ref] Use those conditions when adapting a collection experiment to a particular specimen.

Blank-corrected carbon recovery in polymer tests also needs uncertainty in the background subtraction. Carbon missing from the liquid can have moved to surfaces or gas without being completely converted to carbon dioxide. Conversely, carbon dioxide production establishes conversion of some carbon but does not measure the remaining chain-length distribution. Report closure, identified chemical products and the molar mass distribution as different results; a successful elemental balance alone does not determine the degradation mechanism.

Polyethylene terephthalate, more explicitly poly(ethylene terephthalate), is a polyester made from ethylene-glycol and terephthalate-derived units. It is often called PET polymer in materials contexts. Its chain contains repeated ester connections and para-substituted aromatic rings; it is not polyethylene with a physically mixed additive. ACS identifies the material as a condensation polymer of ethylene glycol and terephthalic acid.^[ref]

An ideal repeat can be writtenwith the two aromatic attachments opposite one another. Counting this repeat gives ${\mathrm{C}}_{10}{\mathrm{H}}_8{\mathrm{O}}_4$. The same count follows from the monomer formulas:This is repeat-unit bookkeeping; exact finite-chain composition also includes the end groups.

Using standard rounded atomic masses, the repeat contributes about $192.17\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$. An original ideal chain with 1000 such repeats therefore has about $192.17\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$ of repeat-unit mass before end-group corrections. A real sample has a molar mass distribution; the repeat count does not assign one molecular mass to every chain.

The ester connections are part of the polymer backbone. Their cleavage by hydrolysis can shorten chains before all products leave the specimen, so retained mass and number-average molar mass need separate observations. Polymer fraction-recovery balance is relevant when soluble fragments and retained material are sampled differently. Neither the polyester label nor a bottle's disappearance from view identifies a degradation mechanism.

An illustrative comparison takes two samples with identical repeat chemistry but different crystallization and processing histories. Their thermal and mechanical responses can differ without a change in the repeat formula. A proposed experiment compares thermal response and chain-distribution measurements under documented conditioning, while checking for hydrolytic change during preparation. This separates molecular identity, chain length and material organization. The derivations here describe an ideal structure; no universal processing temperature or degradation rate is inferred from it.

A polymer fraction-recovery balance accounts for material recovered in each sampled fraction after a polymer experiment, including retained solids, dissolved products, filter deposits and container rinses. It tests whether the fractions used to infer a molar mass distribution represent the intended population. A decrease in retained mass and a change in the number-average molar mass of the analyzed fraction are different observations.

First specify a polymer recovery accounting basis. Comparable dry masses can be summed when they describe the same material inventory; chemical transformation may instead require a conserved-element or repeat-unit inventory. For example, ester hydrolysis incorporates water into new end groups. Summing product mass as though it were unchanged original polymer mass then mixes accounting conventions. The manufacturer's decomposition diagram for polyglycolic acid explicitly distinguishes hydrolytic decomposition from later microbial degradation.^[ref]

For an original closed repeat-unit bookkeeping model with no destruction of those units, let $U_0$ be the initial inventory. WriteHere $r$ is recovery on that specified basis. Material converted into unmeasured chemical products belongs in the unaccounted inventory until measured; a recovery deficit alone does not identify its chemical fate.

On a stipulated consistent mass-equivalent basis, start with 100 mg and recover 70 mg in solids, 20 mg in the soluble fraction and 5 mg in rinses. Recovery is 95%, leaving 5 mg unaccounted. The 30 mg decrease in retained solids is not evidence that all 30 mg was collected as soluble material: only 20 mg was measured there. Experimental mass balance requires those distinctions even when a single residue curve appears smooth.

Combining recovered number-average molar masses also requires counting chains rather than averaging the reported means by mass. If fraction $i$ has mass $m_i$ and correctly measured number-average molar mass $M_{n,i}$, its amount of substance of chains is $m_i/M_{n,i}$. Thus, for the combined measured fractions,An original example recovers 80 mg with $M_n=80\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$ and 20 mg with $M_n=2\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$. These correspond to $1\mu \mathrm{mol}$ and $10\mu \mathrm{mol}$ of chains. Their combined 100 mg divided by $11\mu \mathrm{mol}$ gives $M_n\approx 9.09\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$. The mass-weighted average of the two reported means, $64.4\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$, is not their combined number-average molar mass. Missing fractions with unknown chain counts prevent this calculation from establishing the whole original population's mean.

A useful collection protocol measures initial material, retained residue, filtrate and rinses separately, with preparation blanks and stated drying conditions. Kureha's published water-exposure protocol measures filtered, dried solids, so that observable covers only one part of the balance.^[ref] A size-exclusion chromatography trace of a selected fraction adds another measurement model: IUPAC defines that separation chiefly through hydrodynamic volume in porous non-adsorbing material.^[ref] Recovery, representativeness and the conversion from separation to molar mass must all be justified before interpreting a survivor distribution as the full degraded sample.

A polymer recovery accounting basis specifies the conserved inventory used to compare initial material with recovered fractions. Possible choices include conditioned dry mass, original repeat-unit equivalents or the amount of a particular element. These bases coincide only under suitable chemical and sampling assumptions. A polymer fraction-recovery balance needs that convention before its recovery percentage has a clear meaning.

For fractions $i$ with measured masses $m_i$, suppose $k_i$ converts one unit of that product mass into the chosen original-material equivalent. Recovery on that basis iswhere $B_0$ is the initial inventory in the same units. Taking every $k_i=1$ is a chemical assumption: it requires that the measured masses are directly comparable. Different solvent contents, water incorporated by reaction, salts, fillers or filter residues can invalidate it.

An original polyglycolic acid example makes the distinction visible. Ignoring initial end-group contributions for a repeat-unit bookkeeping comparison, one millimole of ${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{O}}_2$ repeat inventory represents approximately 58.04 mg. Complete ester hydrolysis to one millimole of glycolic acid, ${\mathrm{C}}_2{\mathrm{H}}_4{\mathrm{O}}_3$, gives approximately 76.05 mg. The roughly 18.01 mg difference comes from incorporated water, not extra recovered original repeat inventory. The manufacturer's structural and decomposition diagrams identify the polymer and hydrolysis product.^[ref]

Dividing the product's 76.05 mg directly by 58.04 mg would report approximately 131.0% recovery on mixed bases. The monomer-to-original-repeat conversion is instead $k=58.04/76.05\approx 0.76318$, restoring 58.04 mg of original repeat equivalents. Exact finite-chain accounting must include the original end groups and count hydrolyzed bonds; the repeat-unit example deliberately omits that small-chain correction. Soluble oligomers contain a different number of end groups per repeat, so the monomer conversion is not universal for an unidentified soluble mixture.

Carbon-basis closure for polymer degradation offers another explicit inventory. Each repeat and each glycolic-acid molecule has two carbon atoms, so the example contains approximately 24.02 mg of carbon before and after the specified hydrolysis. If subsequent chemistry produces other carbon-containing products, those products belong in that inventory too. Carbon introduced by solvent or background contamination must be distinguished from specimen carbon; otherwise elemental closure can look satisfactory for the wrong reason.

An original fraction count begins with 1.00 mmol of repeat equivalents and recovers 0.60 mmol in the solid, 0.30 mmol in identified soluble material and 0.05 mmol in rinses. Recovery is 95%, regardless of whether the corresponding product masses differ through hydration. The remaining 0.05 mmol is unaccounted on this basis; the deficit alone does not establish whether it was chemically transformed, escaped collection or was underestimated analytically.

A useful experiment records conditioning and drying, collects filtrate and rinses, identifies the soluble products and measures blanks. Kureha's published test uses filtered, dried residue after timed exposure of material at 2% solids concentration to deionized water.^[ref] That retained-residue mass is one well-defined observable. Inferring the full chemical recovery requires the other fractions and their conversion factors. Report those assumptions separately from the molar mass distribution of whichever fraction was analyzed.

Radical polymerization in which growing chain ends reversibly exchange between active radicals and dormant species. Keeping the active-radical concentration small can reduce bimolecular termination and narrow the molar mass distribution. Termination and chain transfer may still occur, so reversible deactivation alone does not guarantee ideal living polymerization.